Fig. 9
From: Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement
Difference in the orthogonality error \(\left (\log _{10}\!\left |\left \|{\mathbf {I}}\,-\,{\mathbf {Q}}^{\top }{\mathbf {Q}}\right \|_{2}^{(\text {vpa}-16)}-\left \|{\mathbf {I}}-{\mathbf {Q}}^{\top }{\mathbf {Q}}\right \|_{2}^{(\text {Inf})}\right |\right)\) for the case of 16 decimal digits versus “infinite” precision (converted to double). Note that in comparison to Fig. 8, the difference between “infinite” and more than 16 digits is below the machine precision (exact same results)